Mean square endpoint separation of offhyphen;lattice selfhyphen;avoiding walks

摘要

Ten thousand offhyphen;lattice selfhyphen;avoiding walks of 500 steps were generated using a new algorithm combining the features of the enrichment procedure of Wall and Erpenbeck and the dimerization procedure of Alexandrowicz. The mean square endpoint separation was tabulated as a function of the number of steps in the walk and fitted to the equationlang; Rthinsp;N2rang;equals;Athinsp;Nggr;, where N is the number of steps in the walk. A value for ggr; of1.204plusmn; 0.014was obtained, in excellent agreement with values for onhyphen;lattice walks. Earlier investigators using offhyphen;lattice selfhyphen;avoiding walks probably obtained higher values of ggr; because they were limited to 100hyphen;step walks.